hetero and serial corr

# hetero and serial corr - Heteroskedasticity Serial...

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1 Heteroskedasticity & Serial Correlation Slide # 1 * * * * * * * * * * * * * Heteroskedasticity * * Slide # 2 * * * * * * * * Heteroskedasticity & Serial Correlation are Sneaky •C an mess up t-statistics so badly that you might reach wrong conclusions about which independent variables are statistically Slide # 3 significant (i.e., affect dependent variable) and which do not Y * * * * * * * * * * * * Regression line Slide # 4 X * * * * * * * Want dispersion of Want dispersion of dep dep var var around regression around regression line ( σ 2 ) roughly constant across sample NO HETEROSKEDASTICITY Y * * * * * * * * * * * * Regression line Slide # 5 X * * * * * * * NO HETEROSKEDASTICITY Y * * * * * * * * * * * * * * * * * * * Regression line Slide # 6 X * * * * * * * Common case: dispersion of DV around regression line ( σ 2 ) not constant HETEROSKEDASTICITY

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2 Y * * * * * * * * * * * * * * * * * * * Regression line Slide # 7 X * * * * * * * HETEROSKEDASTICITY When can it occur? 9 Example: firm payrolls o Smaller firms – Less variability in payroll sizes – Although firms differ in payroll, the amount of dispersion is limited by the small size of the firms Slide # 8 o Larger firms – More variability in payroll sizes • Greater revenues available for payrolls – Some large firms spend more on payroll – Others spend less – Because base payroll is large, the dispersion between “more” and “less” can be large When can it occur? (cont.) o NOTE: same principle applies for many units with wide range of sizes in same sample – (1) States (population) – (2) Counties (population) Slide # 9 – (3) Colleges (enrollment) – (4) Companies (sales) –(5) Etc . o This is why we expect it in cross-sectional data Consequences • A. If ignore heteroskedasticity in sample • B. Coefficient estimates 9 1. Unbiased - OK Slide # 10 9 2. Consistent – OK 3. Inefficient - not great Consequences (cont.) •C .t - t e s t s 1. The standard errors of estimated coefficients (denominator of t-stats ) are biased and inconsistent, which means . . . Slide # 11 2. t-tests inaccurate Fixes • A. Two approaches 1. Fix only the screwed up standard errors. 1. The idea here is that OLS coefficient estimators remain unbiased so in that regard Slide # 12 , , heteroskedasticity is way less serious than omitted variables bias. 2. But we want to test hypotheses, so we need to get the standard errors right. 3. The solution is “robust” or “heteroskedasticity- consistent” standard errors.
3 Fixes (cont) • A. Two approaches (cont) 2. Fix the coefficients and the standard errors. a. The idea here is that OLS coefficient estimators, although unbiased are inefficient Slide # 13 although unbiased, are inefficient. b. Try to get more efficient estimator. c. The solution is “generalized least squares (GLS).” Detection • White's test 9 1. More general than other tests 9 2. Does not require prior knowledge of form of heteroskedasticity Slide # 14 9 Three versions o #1: uses all X’s, squares and cross-products o #2: uses all X’s and squares o #2: uses only predicted (fitted) y-hat and its square Detection -White’s Test (cont.) 9 3. Hypotheses (always) o a) H 0 : no heteroskedasticity o b) H A : heteroskedasticity exists Slide # 15 White’s Test #1 (cont.) 9 4. Models Used - Preview •(A )Y i = β 0 + β 1 X i1 + β 2 X i2 +u i (first) Slide # 16 •(B -1 ) û

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## This note was uploaded on 11/15/2010 for the course ECO 6416 taught by Professor Staff during the Spring '08 term at University of Central Florida.

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hetero and serial corr - Heteroskedasticity Serial...

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